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Mixing Times for Random Walks on Geometric Random Graphs
Mixing Times Random Walks Geometric Random Graphs
2015/7/10
A geometric random graph, G^d(n,r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each oth...
Average Case Behavior of Random Search for the Maximum
Average Case Behavior Random Search Maximum
2015/7/8
This paper is a study of the error in approximating the global maximum of a Brownian motion on the unit interval by observing the value at randomly chosen points. One point of view is to look at the e...
Simulating the Maximum of a Random Walk
Random walk Single-server queue Simulation Stationary distribution
2015/7/8
In this paper, we show how to exactly sample from the distribution of the maximum of a random walk with negative drift. We also explore related variance reduction methods.
Estimation of Continuous-time Markov Processes Sampled at Random Time Intervals
Method of moments parameter estimation Markov process
2015/7/6
We introduce a family of generalized-method-of-moments estimators of the parameters of a continuous-time Markov process observed at random time intervals. The results include strong consistency, asymp...
Diffusion Approximations for the Maximum of a Perturbed Random Walk
Perturbed random walk diffusion approximation light-tailed distributi
2015/7/6
Considera random walk S=(Sn:n≥O) that is "perturbed" by a stationary sequence (ξn:n≥O) to produce the process S=(Sn+ξn:n≥O). In this paper, we are concerned with developing limit theorems and approxim...
Tail Asymptotics for the Maximum of Perturbed Random Walk
Perturbed random walk Cramér–Lundberg approximation coupling heavy tails
2015/7/6
Consider a random walk S = (Sn:n≥0) that is “perturbed” by a stationary sequence (ξn:n≥0) to produce the process (Sn+ξn:n≥0). This paper is concerned with computing the distribution of the all-time ma...
Complete Corrected Diffusion Approximations for the Maximum of a Random Walk
Corrected diffusion approximations random walks ladder heights single-server queue
2015/7/6
Consider a random walk (Sn: n ≥ 0) with drift −μ and S0= 0. Assuming that the increments have exponential moments, negative mean, and are strongly nonlattice, we provide a complete asymptotic ex...
Capacity of Finite State Channels Based on Lyapunov Exponents of Random Matrices
Finite-state channel hidden Markov model random matrices Shannon capacity
2015/7/6
The finite-state Markov channel (FSMC) is a timevarying channel having states that are characterized by a finitestate Markov chain. These channels have infinite memory, which complicates their capacit...
Uniform Renewal Theory with Applications to Expansions of Random Geometric Sums
Renewal theory random geometric sum corrected diffusion approximation
2015/7/6
Consider a sequence X = (Xn: n ≥ 1)of independent and identically distributed random variables, and an independent geometrically distributed random variable M with parameter p. The random variable SM ...
Efficient Rare-event Simulation for the Maximum of Heavy-tailed Random Walks
State-dependent importance sampling rare-event simulation heavy-tails Lyapunov bounds random walks
2015/7/6
Let (Xn: n ≥ 0) be a sequence of i.i.d. r.v.’s with negative mean. Set S0 = 0 and define Sn = X1 +· · ·+Xn. We propose an importance sampling algorithm to estimate the tail of M = max{Sn: n ≥ 0} that ...
Strongly Efficent Algorithms for Light-tailed Random Walks: An Old Folk Song Sung to a Faster New Tune
Strongly Efficent Algorithms Light-tailed Random Walks Folk Song Sung Faster New Tune
2015/7/6
We revisit a classical problem in rare-event simulation, namely, efficient estimation of the probability that the sample mean of n independent identically distributed light tailed (i.e. with finite mo...
Applying Random Coefficient Models to Strategy Research:Testing for Firm Heterogeneity,Predicting Firm-Specific Coefficients,and Estimating Strategy Trade-Offs
Strategy Mathematical Methods
2015/4/27
Although Strategy research aims to understand how firm actions have differential effects on performance, most empirical research estimates the average effects of these actions across firms. This paper...